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Unformatted text preview: llel servers. I.e., the buffer size
is the same as the number of servers; thus, if all the servers are occupied, then an arriving customer is
rejected. This is the case in the telephone network link model  if all the circuits are busy, an arriving call is
rejected (instead of being queued up if one of them become free later). This is a very important system and
is sometimes known as the loss system. The statetransition diagram is
λ
0 1
µ 3 2
2µ • j = if 0 0 j = j • •
(m–1)µ 3µ Here, In this case, λ λ λ m–1 m mµ j m,1 otherwise.
if 1 0 jm otherwise. j = =j j1! 0 j = 1 ::: m: Since sum of probabilities is 1, we can show that 2m
3,1
X =j 5
0 = 4
:
j! j =0 Speciﬁcally, the probability of an arriving call being blocked is the probability of being in state m:
=m
m!
m =j
j =0 j ! m = P : This is the wellknown ErlangB Blocking/loss formula and is usually denoted by E =
we wrote m. Further, a = = to denote the offered load in Erlang (this is NOT utilization) giving us: E a m = CS 522, v 0.94, d.medhi, W’99 am
m
Pm ! aj :
j =0 j ! 19 The average number in the system, N , is given by N = a1 , E a m: It is interesting to note that the ErlangB loss formual has the following recurrence relation: with the starting point B a 0 = 1: a ,
E a m = m aEaE...
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This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.
 Fall '08
 Staff
 Computer Networks

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